1. Field of the Invention
This invention relates to reducing distortion in monolithic active lowpass filters that use MOS field effect transistors as voltage variable resistors.
2. Description of the Prior Art
Both switched capacitor and continuous-time active filters have been used in large scale, monolithic analog filter applications. Switched capacitor filters provide stable, precise transfer functions with good large signal capability but are often unacceptable because they process discrete time, sampled analog signals, rather than continuous signals. To interface with continuous-time circuits, switched capacitor filters usually require active or passive anti-aliasing and data reconstruction (smoothing) filters.
Continuous-time filters avoid sampling but have other deficiencies. Monolithic continuous-time filters are often active RC circuits that include amplifiers, resistors, and capacitors in a feedback configuration. The frequency response of an RC active filter depends on coefficients that are products of absolute resistance and capacitance values, both of which can be subject to considerable random variation with monolithic processing. However, ratios of resistances and ratios of capcitors remain substantially constant with process variations; therefore, ratios of RC products also remain stable.
A recently developed technique to overcome random coefficient variation is to use field effect transistors (MOSFETs) operated in the nonsaturation (linear) region as electrically variable resistances. An externally variable control voltage applied to the gates of the devices can be used to automatically tune filters to frequency after fabrication or to readjust tuning as coefficients vary with temperature. A more complete discussion of these filters appears in the paper by M. Banu and Y. Tsividis entitled "Fully Integrated Active RC Filters in MOS Technology," IEEE Journal of Solid State Circuits, Vol. SC-18, No. 6, December 1983, to which the reader is referred for background and a detailed analysis.
The drain current of a MOSFET operated in the linear region, as shown in FIG. 2, may be expressed as: ##EQU1## where ##EQU2## I.sub.D is the drain current in the linear region, V.sub.C, V.sub.B, are the gate, substrate, drain, and
V.sub.1, V.sub.2 source potentials with respect to ground, PA1 W and L are the effective channel width and length, that is, the width and length taking into account process variations, such as outdiffusion, that affect the W and L indicated on a layout, PA1 .mu. is the carrier effective mobility in the channel, PA1 V.sub.FB is the flat-band voltage, PA1 N.sub.A is the substrate doping concentration, PA1 C'.sub.ox is the gate oxide capacitance per unit area, PA1 .epsilon..sub.s is the silicon dielectric constant, PA1 q is the electron charge, and PA1 .phi..sub.B is the approximate surface potential in strong inversion for zero backgate bias. (Classically, this potential has been taken to be 2.phi..sub.F with .phi..sub.F the Fermi potential, but .phi..sub.B is actually higher by several kT/q.)
The 3/2 power terms can be expanded as a Taylor series with respect to V.sub.1 and V.sub.2 : ##EQU3##
where the coefficients a.sub.i are independent of V.sub.1 and V.sub.2 and are functions of the gate and substrate potentials and the process and physical parameters of the device.
Expression (2) shows that the drain current is a nonlinear function of the drain to source voltage applied across the device. For small signals, the linear term, Ka.sub.1, predominates, and the device may be treated as a linear conductance, g, as shown in expression (3): ##EQU4##
where the threshold voltage at -V.sub.B backgate bias is given by: EQU V.sub.T =V.sub.FB +.phi..sub.B +.gamma.(-V.sub.B +.phi..sub.B).sup.1/2.
The small-signal conductance of the device depends on the voltage applied to its gate, its effective width-to-length ratio, and other physical parameters related to fabrication. Good matching is achieved by providing all MOSFETs in a particular monolithic circuit with the same gate voltage; monolithic fabrication inherently provides matching of fabrication parameters. Varying the effective W/L ratio then provides a means to obtain different nominal resistances.
Once an active RC filter has been fabricated, its coefficients can be adjusted by varying the gate voltage applied to the MOSFET-resistors. One method that has been used to adjust coefficients is to measure a parameter related to an RC product, such as a phase shift or frequency of oscillation of a test circuit, to compare that quantity to an external reference, and to modify the gate voltage to adjust the measured parameter to the required value. Since all MOSFETs resistors have the same gate voltage, modifying the gate voltage varies the small signal conductances of all MOSFETs simultaneously. While the individual conductances change, their ratios remain constant and are related according to their effective W/L ratios. The RC products also vary but keep the same ratios among themselves. Tuning a single RC product to a known value then suffices to tune an entire filter to the proper frequency. Further advantage can be taken of the inherent tracking in monolithic design by tuning several filters on a single chip with a single gate control voltage.
A prior art limitation in using MOSFETs as resistors has been that the inherent non-linearity severely restricts the peak voltage that may be applied to filters without producing excessive distortion. One approach to reduce distortion in systems has been to attenuate signals before filtering and to boost them after filtering, so that their level never exceeds the signal handling ability of the filter. However, reducing signal level degrades system noise performance. Another approach in the prior art is to use differential filter circuits; these suppress even-order harmonics but increase circuit complexity, size, or power dissipation.
For complex system filtering tasks, there has also been a need in the prior art to combine high-order switched capacitor filters with lower-order continuous-time active RC filters for anti-aliasing and data reconstruction filtering. However, to handle the highlevel signals that are practical and desirable with switched capacitor filtering, there has been a need for compact, continuous-time active RC filters that neither affect noise performance nor increase circuit complexity and size as do prior art designs.